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Revision History for A328307

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Showing entries 1-10 | older changes
a(n) tells how many numbers m there are in range 0..n such that the k-th arithmetic derivative of A276086(m) is zero for some k >= 0.
(history; published version)
#12 by Susanna Cuyler at Sat Oct 12 19:07:15 EDT 2019
STATUS

proposed

approved

#11 by Antti Karttunen at Sat Oct 12 15:19:29 EDT 2019
STATUS

editing

proposed

#10 by Antti Karttunen at Sat Oct 12 15:14:05 EDT 2019
COMMENTS

Although in principle A276086 moves any n out of the "all hope gonelost" zone A100716 (where A328308 is always zero), back to its compelement complement A048103, by comparing the ratio of this and A328309 it can be seen (see the Plot2-link in the Links-section) that such a transfer actually lessens the chances that by just iterating A003415 one could reach zero from there, maybe because A276086 also often transfers its argument to much higher regions, where such chances (of reaching zero) are generally smaller? . Note also how the effect of the primorial base representation can be clearly seen in the folds and warps of that plot.

#9 by Antti Karttunen at Sat Oct 12 13:40:57 EDT 2019
COMMENTS

Although in principle A276086 moves any n out of the "all hope gone" zone A100716 (where A328308 is always zero), back to its compelement A048103, by comparing the ratio of this and A328309 it can be seen (see the Plot2-link) that such a transfer actually lessens the chances that by just iterating A003415 one could reach zero from there. , maybe because A276086 also often transfers its argument to much higher regions, where such chances (of reaching zero) are generally smaller? Note also how the effect of the primorial base representation can be clearly seen in the folds and warps of that plot.

#8 by Antti Karttunen at Sat Oct 12 13:23:37 EDT 2019
COMMENTS

Although in principle A276086 moves any n out of the "all hope gone" zone A100716 (where A328308 is always zero), back to A048103, by comparing the ratio of this and A328309 it can be seen (see the Plot2-link) that such a transfer actually lessens the changes chances that by just iterating A003415 one could reach zero from there. Note also how the effect of the primorial base representation can be clearly seen in the folds and warps of that plot.

#7 by Antti Karttunen at Sat Oct 12 13:22:31 EDT 2019
COMMENTS

Although in principle A276086 moves any n out of the "all hope gone" zone A100716 (where A328308 is always zero), back to A048103, by comparing the ratio of this and A328309 it can be seen (see the Plot2-link) that without such a transfer, actually lessens the changes that by just iterating A003415 one could reach zero from there. Note also how the effect of the primorial base representation can be clearly seen in the folds and warps of that plot.

The effect of the primorial base representation can be clearly seen in the folds and warps of that plot.

#6 by Antti Karttunen at Sat Oct 12 13:20:38 EDT 2019
COMMENTS

The effect of the primorial base representation can be clearly seen in the folds and warps of that plot.

#5 by Antti Karttunen at Sat Oct 12 13:15:35 EDT 2019
COMMENTS

Although in principle A276086 moves any n out of the "all hope gone" zone A100716 (where A328308 is always zero), back to A048103, by comparing the ratio of this and A328309 it can be seen that without such a transfer, there

#4 by Antti Karttunen at Sat Oct 12 13:11:29 EDT 2019
LINKS

<a href="https://oeis.org/plot2a?name1=A328309&amp;name2=A328307&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=0&amp;radiop1=ratio&amp;drawpoints=true">Ratio of A328309(n)/A328307(n) plotted with OEIS Plot2-script</a>

#3 by Antti Karttunen at Sat Oct 12 13:01:36 EDT 2019
LINKS

Antti Karttunen, <a href="/A328307/b328307.txt">Table of n, a(n) for n = 0..65537</a>

FORMULA

For all a(0) = 1; for n >= 0, a(A328116(n)) = a(n-1) + A328306(n).

For all n >= 0, a(A328116(n)) = n.